1. Field of the Invention
The present invention relates to a discrete cosine transformation (DCT) system and a discrete cosine inverse transformation (IDCT) system performing an inverse discrete cosine transformation, more particularly relates to a discrete cosine transformation system and a discrete cosine inverse transformation system having a simple circuit structure and preferably able to perform a higher speed operation.
As the discrete cosine transformation system and discrete cosine inverse transformation system in the present invention, the present invention relates to (1) a two-dimensional 4 row.times.8 column discrete cosine transformation (4.times.8 DCT) system, and an inverse transformation (4.times.8 IDCT) system thereof; (2) a two-dimensional 4 row.times.4 column discrete cosine transformation (4.times.4 DCT) system, and an inverse transformation (4.times.4 IDCT) system thereof; and (3) a discrete cosine transformation system which carries out both of the two-dimensional 8 row.times.8 column discrete cosine transformation and two-dimensional 4 row.times.8 column discrete cosine transformation, and an inverse transformation system for them.
2. Description of the Related Art
The discrete cosine transformation system which performs transformation from a real domain (space) to a frequency domain (space) and discrete cosine inverse transformation system which is an inverse transformation thereof are known as one type of orthogonal transformations and are used in for example image processing.
For example, as one example of the discrete cosine transformation system apparatus and discrete cosine inverse transformation system, examples will be shown for the two-dimensional 4 row.times.8 column discrete cosine transformation (4.times.8 DCT) and two-dimensional 4 row.times.8 column discrete cosine inverse transformation (or two-dimensional 4 row.times.8 column inverse discrete cosine transformation: 4.times.8 IDCT).
The two-dimensional 4.times.8 DCT and two-dimensional 4.times.8 IDCT are defined in the following equation 1 and equation 2, respectively. EQU DCT: [C]=(1/4) [P][X].sup.t [N] (1) EQU IDCT: [X]=(1/2).sup.t [P][C][N] (2)
Here, the matrix [C] contains matrix data arranged in a 4 row.times.8 column frequency domain, and the matrix [X] contains original (input) matrix data in a 4 rows.times.8 columns real domain. The matrix [P] denotes a 4 rows.times.4 columns constant matrix data for the transformation, and the matrix [N] denotes constant matrix data consisting of rows.times.8 columns for transformation. The suffices t on the left top indicate an transposition matrix. Namely, .sup.t [N] represents a transposition matrix of the matrix [N], and, .sup.t [P] represents a transposition matrix of the matrix [P].
The matrix [N] is defined by the following equation 3. ##STR1##
The coefficients (factors) in equation 3 are defined as shown in Table 1.